The zweibein formulation of Carrollian geometries is discussed in [1]}, [2]}, [3]}. In the zweibein formulation, a \((1+1)\)  dimensional Carrollian geometry is described by the zweibeins \(e^0_{\alpha }(\tau ,\sigma )\)  and \(e^1_{\alpha }(\tau ,\sigma )\) , with their inverses \(e^{\alpha }_0(\tau ,\sigma )\)  and \(e^{\alpha }_1(\tau ,\sigma )\)  defined through the relations
\(e^0_{\alpha }e^{\alpha }_0 = 1, \quad e^1_{\alpha }e^{\alpha }_1 = 1, \quad e^0_{\alpha }e^{\alpha }_1 = 0, \quad e^1_{\alpha }e^{\alpha }_0 = 0, \quad e^0_{\alpha }e^{\beta }_0 + e^1_{\alpha }e^{\beta }_1 = \delta ^{\beta }_{\alpha }.\) 
